Question

A $5000, 14.5% bond with semi-annual coupons redeemable at par on August 1, 2022, was purchased on March 5, 2011, at 95.5. What was the approximate yield rate?

The approximate yield rate was %.

(Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

Answer #1

Face Value, F = $ 5,000

Price, P = $ 95.5

Coupon Rate = 14.5 %

Semi-annual coupon rate = 14.5 % / 2 = 7.25 %

Coupon Payment, C = 7.25 % off $ 5000 = $ 362.5

Issue Date = March 5 2011

Redemption Date = August 1 2022

No. of years = 11 years 146 days

No. of semi-annual periods = ( 11 * 2 ) + ( 146 / 182 ) = 22 + 0.8022 = 22.8022

**Note: 146 days is 0.8022 of a semi-annual period (
365 / 2 = 182 days )**

Now,

Approximate Yield = [ C + { ( F - P ) / n } ] / [ (F + P) / 2 ]

= [ 362.5 + { (5000 - 95.5) / 22.8022 } ] / [ (5000 + 95.5) / 2 ]

= 22.6705 %

Since, the above yield to maturity is for semi-annual period, we need to convert it for annual periods.

Hence, Approximate yield = 22.6705 % * 2 = 45.3411 % [ this is an approximate yield as solved on pen and paper]

As per the excel calculations, the exact yield rate is 42.4642 %

A $5000, 14.5% bond with semi-annual coupons redeemable at par
on August 1, 2022, was purchased on March 5, 2011, at 95.5. What
was the approximate yield rate?
The approximate yield rate was?
(Round the final answer to four decimal places as needed. Round
all intermediate values to four decimal places as needed.)

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(Round the final answer to the nearest cent as needed. Round
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(Round the final answer to the nearest cent as needed. Round
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Already worked but not correct in chegg.

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